Back
 AJCM  Vol.3 No.3 , September 2013
Finite Element Analysis of the Ramberg-Osgood Bar
Abstract: In this work, we present a priori error estimates of finite element approximations of the solution for the equilibrium equation of an axially loaded Ramberg-Osgood bar. The existence and uniqueness of the solution to the associated nonlinear two point boundary value problem is established and used as a foundation for the finite element analysis.
Cite this paper: D. Wei and M. Elgindi, "Finite Element Analysis of the Ramberg-Osgood Bar," American Journal of Computational Mathematics, Vol. 3 No. 3, 2013, pp. 211-216. doi: 10.4236/ajcm.2013.33030.
References

[1]   W. R. Osgood and W. Ramberg, “Description of Stress-Strain Curves by Three Parameters,” NACA Technical Note 902, National Bureau of Standards, Washington DC, 1943.

[2]   L. A. James, “Ramberg-Osgood Strain-Harding Characterization of an ASTM A302-B Steel,” Journal of Pressure Vessel Technology, Vol. 117, No. 4, 1995, pp. 341-345. doi:10.1115/1.2842133

[3]   K. J. R. Rasmussen, “Full-Range Stress-Strain Curves for Stainless Steel Alloys,” Research Report R811, University of Sydney, Department of Civil Engineering, 2001.

[4]   V. N. Shlyannikov, “Elastic-Plastic Mixed-Mode Fracture Criteria and Parameters, Lecture Notes Applied Mechanics, Vol. 7,” Springer, Berlin, 2002.

[5]   P. Dong and L. DeCan, “Computational Assessment of Build Strategies for a Titanium Mid-Ship Section,” 11th International Conference on Fast Sea Transportation, FAST, Honolulu, 26-29 September 2011, pp. 540-546.

[6]   P. Dong, “Computational Weld Modeling: A Enabler for Solving Complex Problems with Simple Solutions, Keynote Lecture,” Proceedings of the 5th IIW International Congress, Sydney, 7-9 March 2007, pp. 79-84.

[7]   E. Zeidler, “Nonlinear Functional Analysis and Its Applications, Variational Methods and Optimization, Vol. III,” Springer Verlag, New York, 1986. doi:10.1007/978-1-4612-4838-5

[8]   R. A. Adams, “Sobolev Spaces, Pure and Applied Mathematics, Vol. 65,” Academic Press, Inc., New York, San Francisco, London, 1975.

[9]   V. G. Maz’Ja, “Sobolev Spaces,” Springer-Verlag, New York, 1985.

[10]   F. E. Browder, “Variational Methods for Non-Linear Elliptic Eigenvalue Problems,” Bulletin of the American Mathematical Society, Vol. 71, 1965, pp. 176-183. doi:10.1090/S0002-9904-1965-11275-7

[11]   R. Temam, “Mathematical Problems in Plasticity,” Gauthier-Villars, Paris, 1985.

[12]   G. Strang and G. J. Fix, “An Analysis of the Finite Element Method,” Prentice-Hall, Inc., Englewood Cliffs, 1973.

[13]   P. G. Ciarlet, “The Finite Element Method for Elliptic Problems,” North-Holland, Amsterdam, 1978.

[14]   J. T. Oden And G. F. Carey, “Finite Elements,” Prentice-Hall, Englewood Cliffs, 1984.

[15]   S. C. Brenner and L. R. Scott, “The Mathematical Theory of Finite Element Methods, Texts in Applied Mathematics, v. 15,” 3rd Edition, Springer Verlag, New York, 2008. doi:10.1007/978-0-387-75934-0

 
 
Top